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A234509
2*binomial(9*n+6,n)/(3*n+2).
8
1, 6, 69, 992, 15990, 276360, 5006386, 93817152, 1803606255, 35373572460, 704995403541, 14236901646240, 290687378847684, 5990903682047592, 124463414269524000, 2603845580096662656, 54807372993836345589, 1159856934027109448130, 24663454505518980363102, 526708243449729452311200, 11291926596343014148087470
OFFSET
0,2
COMMENTS
Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=9, r=6.
LINKS
J-C. Aval, Multivariate Fuss-Catalan Numbers, arXiv:0711.0906v1, Discrete Math., 308 (2008), 4660-4669.
Thomas A. Dowling, Catalan Numbers Chapter 7
Wojciech Mlotkowski, Fuss-Catalan Numbers in Noncommutative Probability, Docum. Mathm. 15: 939-955.
FORMULA
G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=9, r=6.
MATHEMATICA
Table[6 Binomial[9 n + 6, n]/(9 n + 6), {n, 0, 30}]
PROG
(PARI) a(n) = 2*binomial(9*n+6, n)/(3*n+2);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(3/2))^6+x*O(x^n)); polcoeff(B, n)}
(Magma) [2*Binomial(9*n+6, n)/(3*n+2): n in [0..30]];
KEYWORD
nonn
AUTHOR
Tim Fulford, Dec 27 2013
STATUS
approved